Advanced development of a pressurized ash agglomerating fluidized-bed coal gasification system. Quarterly progress report, April 1-June 30, 1982 Page: 87 of 105
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A model was also developed to describe this gas leakage phenomenon from the
bubble by assuming that the gas leaks out through the bubble boundary at a
superficial velocity equivalent to the superficial minimum fluidization
velocity. For a semi-spherical bubble, the rate of change of bubble volume
can be expressed as:
dV - D 12
dt = G - Umf 2
where for a semi-spherical bubble.
Equation (1) can be reduced, after a few mathematical manipulations, to show
the changes of bubble diameter with respect to time in equation (2):
DB 2 dDB dt(2)
(4G - 2 T Umf DB2 (2
Integrating equation (2) with the boundary condition that DB = 0 at t = 0
gives 2G + DB Tr U
12 G + D2G -GDm f
t =U 2nG~m Pn (2G - DB 2rGUm ) - DB - (3)
U mf - DB
The maximum bubble size, where the total gas leakage through the bubble
boundary is equal to the total jet flow, can be obtained from either equation
(1) or equation (3) to be:
max Um f. (4)
The total amount of gas leaks out of the bubble at a bubble size DB can be
found from: lTD 2
dF = Umf 2 dt
f2Umf DBD d DD (5)
2 (4G - 2nUmfDB2 )
Integration of equation (5) with the boundary condition that DB = 0 at
t = 0, results in:
2G + DB 2yfGU B
F = Gn (2G - DB )- DB - 12 (6)
Umf V ZGWmr (2-B 2n1~m
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Advanced development of a pressurized ash agglomerating fluidized-bed coal gasification system. Quarterly progress report, April 1-June 30, 1982, report, October 21, 1982; United States. (https://digital.library.unt.edu/ark:/67531/metadc1058542/m1/87/: accessed May 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.